We know that Hawthorne tells the reader on several occasions that the letter A represents different things. I can't recall Hawthorne saying adultery was one of those things.
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No, I don't think he ever actually uses the word adultery. I think given the circumstances, the "A" would have represented this sin though.
Thanks Aslan for your reply. I am working on a piece that looks at the Scarlet Letter in a postmodern way. I am suggesting that the A does not represent Adultery. It represents something altogether different and there is ample reason to believe that Hawthorne didn't mean it to be for adultery either.